Home schooling is legal in the United States. A factor in its favor is that to win in court, a state would have to show that the standard used to prevent home schooling was the same as the one under which they close down a public school for underachievement, so in effect, the American “social pass” makes it impossible to meaningfully regulate home school. Local bodies often resent home schoolers since it deprives them of revenue (lost since otherwise the student would go to public school, and bring in lots of money in aid), but a clearly hareidim parent won’t generate a problem.
The costs can be prohibitive. If the parents are college educated (degreed or not), with a strong yeshiva and seminary problem, then fine – but otherise they might end up hiring tutors. If the mother of the house wants to home school, and would otherwise be a housewife, the cost isn’t great, but if she is giving up $100K to stay home with the kids, its likely that schools are cheaper.
As Jews have an ancient tradition of parents learning with their children, home schooling should be easier for us (among goyim, the idea of parents teaching their children is considered weird).